U.S. Pat. No. 4,810,232, issued Mar. 7 1989 and assigned to the assignee of this invention, describes a stroking constant velocity universal joint suitable for application at the inboard location of a front wheel drive axle of a motor vehicle. The universal joint includes an outer drive member or tulip housing usually connected to a transaxle differential of the motor vehicle and an inner drive member or spider on an axle shaft. The spider has three radial trunnions reaching into three longitudinal drive channels in the tulip housing. A cylindrical drive roller in each longitudinal drive channel is mourned on a corresponding one of the radial trunnions for rotation about a radial centerline thereof by a full complement of needle-type roller bearings ("needle bearings") parallel to the radial centerline between a cylindrical bearing race on the trunnion and a radial bore in the drive roller. A full complement of needle bearings is the maximum number of needle bearings which can simultaneously engage the bearing race while maintaining a minimum bearing-to-bearing clearance necessary to prevent binding. The radial bore in each roller has an inner convex surface, flaring radially out from a minimum diameter at the crown of the convex surface at the middle of the radial bore to a maximum diameter at each end thereof, so that the drive rollers are permitted to tip relative to the corresponding radial centerlines. The radial clearance between the needle bearings and the surrounding convex surface, however, affords the needle bearings more latitude to skew, i.e. become non-parallel to the corresponding radial centerline, than otherwise obtains where the radial bore in the drive roller defines a plain cylinder closely surrounding the needle bearings. A stroking constant velocity universal joint according to this invention is an improvement relative to the stroking constant velocity universal joint described in the aforesaid U.S. Pat. No. 4,810,232.